BCCHS Curriculum Map1. What are our Core Values:

Rigor, Community, Real World Connections, Global Citizenship2. Connecting our Curricula to our Core Values3. How Can We be Lifelong Learners?

Advanced Topics in MathematicsTeacher: Elisabeth Jaffe / Tammy Wen

2015-16Year-Long Essential Questions

Essential Questions Content Skills & Standards

Assessment Materials/Resources

How can we make sure we are never wrong?

How can we use numbers to demonstrate life and love in our world?

Is it possible to keep our secrets a secret? Why can’t we predict the future? Can we use mathematics to describe human

social behavior? We answer each of these questions using the Five Habits of MindPerspective - what are the different methods we can use to solve problems?Evidence - prove your answersSignificance - why are we solving these problems?Connections - what does this remind me of? how does this change or influence other things we do?Supposition - alternatives? what if...?

- Statistics- Mathematical

Reasoning- Set Theory- Matrices- Cryptology- Graph Theory- Chaos Theory- Game Theory- Non-Euclidean

Geometry- PreCalculus

MP 1-8 HomeworkExamsClass ParticipationProjects

Einstein’s Dreams / The Housekeeper and the ProfessorBudgeting ProjectBCSM ProposalStatistical Analysis

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BCCHS Curriculum Map1. What are our Core Values:

Rigor, Community, Real World Connections, Global Citizenship2. Connecting our Curricula to our Core Values3. How Can We be Lifelong Learners?

Timeframe: 2 weeksUnit 1: Statistics

Essential Questions Skills & Standards Assessment Materials/Resources School Values*

How can we understand data relationships so as not to be manipulated by the media?

How can we determine our academic success using the normal curve and standard deviation?

Is there a relationship between two seemingly unrelated sets of data?

What is an acceptable margin of error when looking at statistical data?

What are the connections between probability and statistics?

• Standard 1 Make sense of problems and persevere in solving them. • Standard 2 Reason abstractly and quantitatively. • Standard 3 Construct viable arguments and critique the reasoning of others. • Standard 4 Model with mathematics. • Standard 6 Attend to precision. • Standard 7 Look for and make use of structure.

Unit Test

Class discussion

Class Notes

Homework

Group Work

Questions

PROJECT: Decision Making

Mathematical Fallacies and Paradoxes by Bryan Bunch

Why do Buses Come in Threes by Robert Eastaway & Jeremy Wyndham

Calculated Risks: How to Know When Numbers Deceive You by Gerd Gigerenzer

http://www.khanacademy.org/math/statistics?k

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*In this unit I implement all of our core values. We begin the unit by discussing the way statistical information is presented to the public, primarily medical information and voter polls. We talk about percentages versus ratios. We discuss methods of representation. We determine the best samples and distributions. All of these things allow students to see real world connections. It also allows them to become global citizens because they learn how to present information and what they need to look for in data to know if we need to bring about change and in what areas. Students also work together to analyze statistical data to determine fallacies. This will affect the way they make decisions. They are engaged in sophisticated discussions (rigor), but they are also looking at whether or not data is used to effectively communicate information.

BCCHS Curriculum Map1. What are our Core Values:

Rigor, Community, Real World Connections, Global Citizenship2. Connecting our Curricula to our Core Values3. How Can We be Lifelong Learners?

Timeframe: 2 weeksUnit 2: Mathematical Reasoning

Essential Questions Skills & Standards Assessment Materials/Resources School Values

How can we make sure we are never wrong?

- What rules must we follow when we make an argument?

- How do we determine the best approach to making an argument?

- How can we solve recursive problems, such as the Towers of Hanoi?

- What is a proof by induction?

•F.BF.1b

• Standard 1 Make sense of problems and persevere in solving them. • Standard 2 Reason abstractly and quantitatively. • Standard 3 Construct viable arguments and critique the reasoning of others. • Standard 4 Model with mathematics. • Standard 5 Use appropriate tools strategically. • Standard 6 Attend to precision. • Standard 7 Look for and make use of structure. • Standard 8 Look for and express regularity in repeated reasoning.

Unit Test

Class Discussion

Class Notes

Group Discussion

Homework

Questions

How Long is a Piece of String by Robert Eastaway & Jeremy Wyndham

Why do Buses Come in Threes by Robert Eastaway & Jeremy Wyndham

Thinking in Numbers by Daniel Tammet

One Equals Zero by Nitsa Movshovitz-Hadar

R, C, RWC

BCCHS Curriculum Map1. What are our Core Values:

Rigor, Community, Real World Connections, Global Citizenship2. Connecting our Curricula to our Core Values3. How Can We be Lifelong Learners?

Timeframe: 3 weeksUnit 3: Set Theory

Essential Questions Skills & Standards Assessment Materials/Resources School Values

How can we use numbers to demonstrate life and love in our world?

- What information can be represented by a set?

- What are different ways of combining sets to obtain new information?

- How can we represent a function using a set?

- What are different ways of representing a set?

- How can we find inverses and compositions of functions using sets?

- How is a sequence a set?

• F.IF.7

• Standard 1 Make sense of problems and persevere in solving them. • Standard 2 Reason abstractly and quantitatively. • Standard 3 Construct viable arguments and critique the reasoning of others. • Standard 4 Model with mathematics.

Unit Tests

Class Discussion

Group Discussion

Class Notes

Homework

Questions

The Language of Mathematics by Keith Devlin

Discrete Mathematics and Its Applications by Kenneth Rosen

Elementary Number Theory by Kenneth Rosen

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BCCHS Curriculum Map1. What are our Core Values:

Rigor, Community, Real World Connections, Global Citizenship2. Connecting our Curricula to our Core Values3. How Can We be Lifelong Learners?

Timeframe: 2 weeksUnit 4: Matrices

Essential Questions Skills & Standards Assessment Materials/Resources School Values

How can we model the way we communicate with each other?

- What is a matrix?- How can we perform arithmetic

operations on a matrix?- What are different types of

matrices?- How can we use a matrix as a

method of communication?- How do we solve systems of

equations using matrices?

• N.VM• A.REI.8, 9

• Standard 1 Make sense of problems and persevere in solving them. • Standard 2 Reason abstractly and quantitatively. • Standard 4 Model with mathematics. • Standard 7 Look for and make use of structure. • Standard 8 Look for and express regularity in repeated reasoning.

Unit Test

Group Discussion

Class Discussion

Class Notes

Homework

Questions

Discrete Mathematics and Its Applications by Kenneth Rosen

Elementary Number Theory by Kenneth Rosen

https://www.khanacademy.org/math/linear-algebra

R, RWC, C, GC

BCCHS Curriculum Map1. What are our Core Values:

Rigor, Community, Real World Connections, Global Citizenship2. Connecting our Curricula to our Core Values3. How Can We be Lifelong Learners?

Timeframe: 3 weeksUnit 5: Cryptology

Essential Questions Skills & Standards Assessment Materials/Resources School Values

Is it possible to keep our secrets a secret?

- What is modular?- How do we perform modular

arithmetic? - What is the Caesar transformation?- What are Block and Stream

ciphers?- How can secret keys be used in

cryptology?

• A.CED.1, 2, 3, 4

• Standard 1 Make sense of problems and persevere in solving them. • Standard 2 Reason abstractly and quantitatively. • Standard 4 Model with mathematics. • Standard 5 Use appropriate tools strategically. • Standard 7 Look for and make use of structure. • Standard 8 Look for and express regularity in repeated reasoning.

Unit Test

Group Discussion

Class Discussion

Class Notes

Homework

Questions

Innumeracy by John Allen Paulos

Once Upon a Number by John Allen Paulos

Elementary Number Theory by Kenneth Rosen

R, RWC

BCCHS Curriculum Map1. What are our Core Values:

Rigor, Community, Real World Connections, Global Citizenship2. Connecting our Curricula to our Core Values3. How Can We be Lifelong Learners?

Timeframe: 2 weeksUnit 6: Graph Theory

Essential Questions Skills & Standards Assessment Materials/Resources School Values*

Is it possible to visualize a social network?

- What can be represented by a graph?

- How do we disseminate information?

- How can we model social networking?

- How can we develop new graphs from old ones?

- In what other ways can we represent a graph?

- What does a path on a graph tell us?

- How do we find the shortest way to get from one place to another?

- What is the purpose of a circuit?- How can we use a graph to predict

the spread of a virus?- How can we use graph coloring to

create a schedule?

• Standard 1 Make sense of problems and persevere in solving them. • Standard 6 Attend to precision. • Standard 7 Look for and make use of structure. • Standard 8 Look for and express regularity in repeated reasoning.

Unit Test

Group Discussion

Class Discussion

Class Notes

Homework

Questions

Discrete Mathematics and Its Applications by Kenneth Rosen

Graph Theory and Its Applications by Jonathan Gross

R, RWC, GC

BCCHS Curriculum Map1. What are our Core Values:

Rigor, Community, Real World Connections, Global Citizenship2. Connecting our Curricula to our Core Values3. How Can We be Lifelong Learners?

Timeframe: 2 weeksUnit 7: Chaos Theory

Essential Questions Skills & Standards Assessment Materials/Resources School Values

Why can’t we predict the future?

- What is self-organization?- What powers do the powerless

possess?- What is a fractal?- Where do we see natural fractals?- How can we represent time with

fractals?- What is the significance of what is

missing?

• N.CN.3, 4, 5, 6

• Standard 2 Reason abstractly and quantitatively. • Standard 3 Construct viable arguments and critique the reasoning of others. • Standard 4 Model with mathematics. • Standard 7 Look for and make use of structure. • Standard 8 Look for and express regularity in repeated reasoning.

Unit Test

Group Discussion

Class Discussion

Homework

Questions

Concepts of Modern Mathematics by Ian Stewart

Coincidences, Chaos, and All That Math Jazz by Edward B. Burger, Michael Starbird, & Alan Witschonke

Seven Life Lessons of Chaos by John Briggs and David Peat

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BCCHS Curriculum Map1. What are our Core Values:

Rigor, Community, Real World Connections, Global Citizenship2. Connecting our Curricula to our Core Values3. How Can We be Lifelong Learners?

Timeframe: 4 weeksUnit 8: Game Theory

Essential Questions Skills & Standards Assessment Materials/Resources School Values

Can we use mathematics to describe human social behavior?

- What is universal to all games we study?

- How can we use trees to represent games?

- What can we use to determine the best choice at any given point during a game?

- What are sequential games?- What are the dangers of price

competition?- What happens in simultaneous

games?- What are massive coordination

games?- What is the Prisoner’s Dilemma?- What is adverse selection?- How can we negotiate effectively?

• Standard 1 Make sense of problems and persevere in solving them. • Standard 2 Reason abstractly and quantitatively. • Standard 3 Construct viable arguments and critique the reasoning of others. • Standard 4 Model with mathematics. • Standard 5 Use appropriate tools strategically. • Standard 6 Attend to precision. • Standard 7 Look for and make use of structure. • Standard 8 Look for and express regularity in repeated reasoning.

Unit Test

Group Discussion

Class Discussion

Class Notes

Homework

Questions

An Introduction to Game Theory by Martin Osborne

Game Theory at Work by James Miller

R, RWC

BCCHS Curriculum Map1. What are our Core Values:

Rigor, Community, Real World Connections, Global Citizenship2. Connecting our Curricula to our Core Values3. How Can We be Lifelong Learners?

Timeframe: 2 weeksUnit 9: Non-Euclidean Geometry

Essential Questions Skills & Standards Assessment Materials/Resources School Values

When our assumptions about geometrical ideas change, can we develop a more logical way of explaining the world?

- What are the logical deficiencies in Euclidean Geometry?

- How does Euclid’s parallel postulate define geometry?

- What happens when parallel lines cross once?

- What happens when parallel lines cross an infinite number of times?

- How can we show the sum of the angles in a triangle?

- Why are other geometries more logically consistent with the world we live in?

• G.GPE.3

• Standard 2 Reason abstractly and quantitatively. • Standard 5 Use appropriate tools strategically. • Standard 6 Attend to precision. • Standard 7 Look for and make use of structure.

Unit Test

Class Discussion

Class Notes

Group Discussion

Homework

Questions

Introduction to Non-Euclidean Geometry by Harold Wolfe

Basics Concepts of Geometry by Walter Prenowitz and Meyer Jordan

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BCCHS Curriculum Map1. What are our Core Values:

Rigor, Community, Real World Connections, Global Citizenship2. Connecting our Curricula to our Core Values3. How Can We be Lifelong Learners?

Timeframe: 3 weeksUnit 10: PreCalculus

Essential Questions Skills & Standards Assessment Materials/Resources School Values

What information is essential to studying change in our world?

- Where do numerical patterns exist in our natural world?

- How can we describe and distinguish between different arithmetic sequences?

- How can we describe and distinguish between different geometric sequences?

- How are arithmetic and geometric sequences related?

- How can we use patterns in a series to find the sum?

- What do we use to distinguish series of numbers in an abbreviated way?

- What is a limit?- How can we use a limit to determine

the sum of an infinite series?- What are some properties of sigma

notation that will help us find sums more easily?

• A.REI.2• A.REI.11• F.BF.3, 4a• F.TF.1, 2• F.TF.5• F.TF.8

• Standard 1 Make sense of problems and persevere in solving them. • Standard 3 Construct viable arguments and critique the reasoning of others. • Standard 4 Model with mathematics. • Standard 6 Attend to precision. • Standard 7 Look for and make use of structure.

Unit Test

Class discussion

Notes

Homework

Group Work

Questions

Coincidences, Chaos, and All That Math Jazz by Edward B. Burger, Michael Starbird, & Alan Witschonke

The Math Book by Clifford Pickover

R, RWC, C, GC